D. A. Gates, R. B. White NSTX Physics Meeting 1/19/03 Collisional transport in a low aspect ratio tokamak- beyond the drift kinetic formalism D. A. Gates, R. B. White NSTX Physics Meeting 1/19/03

Outline Motivation Method Inputs Results Benchmarks  surprise Control System Speedup Motivation Method Inputs Results Benchmarks  surprise Implications

Control System Speedup Characterized system delays Changed output communication method from VME backplane to FPDP (Front Panel Data Port) Built New interface module to bridge from FPDP output to (ancient home-made) power supply link Split the link into four parallel links to avoid communication pileup Replaced Sky computer FPDP cards to a more recent version (lower latency i/o control) Rewrote communication software to take advantage of the hardware improvements

Measured latency Measured latency has been reduced to ~1/4 of original value Some hope for further improvements with existing hardware Should be sufficient for vertical position control, RWM may need better performance System used during TF test: measured latency = 1.2ms = tps + tcontrol < t > = 0.680ms < t > = 1.39ms < t > = 2.9ms

Motivation Much recent discussion on whether anomalous ion heating exists in NSTX Argument rests on whether ci < ci_neo In spherical tokamak geometry, the toroidal Larmor radius rif ~ rb ~ e1/2riq (banana width) (See, e.g., Mikkelsen, White, Akers, et al. Phys. Plasmas 4 (1997) 3667 Violates the primary assumption of neoclassical theory (See, e.g., Hinton and Hazeltine, Rev. Mod. Phys. 48 (1976) 239 - Sec IIB) Neoclassical theory not valid in an ST! Need full orbit calculation - omniclassical theory Intuition is ci_omni > ci_neo

Method Compare the diffusivity as calculated by a full orbit code (GYRO) with those calculated by a orbit average code (ORBIT) ORBIT - solves gyro-averaged Hamiltonian in Boozer coordinates with collisions GYRO - solves Newton’s equations with Lorentz force on XY grid with collisions

NSTX Equilibria Two disparate well characterized equilibria chosen High current, low field (1.2MA , 0.3T) High field, low current (0.45T , 0.8MA) Expect larger change in diffusivity since |Bf/Bq| smaller

Orbits rif ~ 4rb for high current low field case much larger step size for transport Banana width = 1.1cm Full orbit width = 5.2cm

Diffusivity calculation Insert 2000 particles, E = 1.1keV, f(y,q) = d(y), with random initial pitch Measure diffusivity as slope of RMS deviation from initial flux surface GYRO ORBIT <xN2> = Ncolll2 l = (<v>Dt)/Ncoll  <xN2> = vlDt (1) G = [n(r+l) - n(r-l)]v = vldn/dr G = -D[dn/dr]  D = vl (2) D = <xN2> /Dt (3) <xN2> = S(dy/(dy/dr))2

Diffusivity profiles High current low field (108989) Repeat calculation at 10 different radii for each equilibrium using both codes Plot the ratio of omni - neoclassical diffusion vs. normalized poloidal flux Omniclassical diffusion is up to ~2.5 times larger than neoclassical High current low field (108989) High field low current (108730)

Ongoing studies In core of device r* ~ 0.01 Leads to non-conservation of m Collisionless diffusion exists Strong dependence of omni - neoclassical ratio on n* when outside banana regime wb/wc ~ T-1/2

Benchmark of collision operators Different collision operators require comparison Fix particles in space but allow to diffuse in velocity space Verify equipartition reached on same timescale Lorentz collision operator for guiding center code Random scatter Dv on surface of sphere with radius v for full orbit code Dv v1 |v1| = |v2| v2

Benchmark against high aspect ratio neoclassical theory But it doesn’t! Expect that as e  0 and r*  0 that omniclassical  neoclassical Neoclassical is wrong! For more see R.B. White Theory seminar Feb. 5

Summary We have demonstrated that neoclassical theory cannot be used to accurately describe the minimum possible collisional transport in a spherical tokamak. Tokamak tools of little use! We have called the corrected diffusivity “omniclassical” (or all - classical) Amazingly, the extrapolation of this result to high aspect ratio has uncovered a fundamental flaw with neoclassical theory at high aspect ratio

Summary (cont.) Omniclassical transport is greater than neoclassical at low aspect ratio - strengthening the argument for the existence of an anomalous ion heating mechanism on NSTX